Lesson H1-H3

H1-H3 Fundamental Theorem, definite integrals and areas Quiz: AQA Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson H1-H3, Fundamental Theorem, definite integrals and areas: 20 multiple choice questions for the AQA Maths (7357), Unit 8: Integration, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. The Fundamental Theorem of Calculus links integration and differentiation. If F'(x) = f(x), what is the integral of f(x) from a to b?

    • F(b) + F(a)
    • F(a) - F(b)
    • F'(b) - F'(a)
    • F(b) - F(a)

  2. If F(x) is the integral from a to x of f(t) dt, what is dF/dx?

    • f(x)
    • x f(x)
    • F(x) - F(a)
    • f(a)

  3. Evaluate the integral from 1 to 3 of 2x dx.

    • 8
    • 9
    • 4
    • 6

  4. Evaluate the integral from 0 to pi of sin x dx.

    • pi
    • 0
    • -2
    • 2

  5. Evaluate the integral from 0 to 1 of e^(2x) dx.

    • 2e^2 - 2
    • e^2 - 1
    • e^2/2
    • (e^2 - 1)/2

  6. If f(x) is negative for all x in [a, b], what is the sign of its definite integral?

    • Zero
    • Positive
    • Undefined
    • Negative

  7. To find the area between upper curve y = f(x) and lower curve y = g(x), integrate what?

    • g(x) - f(x)
    • f(x) - g(x)
    • f(x) + g(x)
    • f(x) × g(x)

  8. Find the area between y = 4 - x^2 and the x-axis for 0 <= x <= 2.

    • 16/3
    • 8/3
    • 32/3
    • 8

  9. Find the area enclosed between y = x and y = x^2 for 0 <= x <= 1.

    • 1/3
    • 5/6
    • 1/6
    • 1/2

  10. For what positive value of k is the integral from 0 to k of 3x^2 dx equal to 8?

    • 4
    • 8
    • 3
    • 2

  11. Evaluate the integral from 1 to 4 of 1/x dx.

    • ln 3, approximately 1.099
    • ln 4, approximately 1.386
    • 3
    • 3/4, approximately 0.75

  12. A particle has velocity v = 3t^2 m/s. What is its displacement change from t = 1 s to t = 2 s?

    • 7 m
    • 3 m
    • 8 m
    • 9 m

  13. Find the area between y = e^x and y = 1 for 0 <= x <= 1.

    • e - 2
    • e - 1
    • 2 - e
    • e

  14. What type of variable is x in the definite integral of f(x) from a to b?

    • Dummy variable
    • Constant variable
    • Dependent variable
    • Free variable

  15. Find the area enclosed between the curve y = x(x - 2) and the x-axis.

    • 2
    • 4/3
    • 8/3
    • -4/3

  16. Find the area enclosed between y = x^2 and y = 2x - x^2.

    • 1/6
    • 2/3
    • 1/3
    • 1

  17. Find the value of a, with a not equal to 2, such that the integral from a to 2 of 2x dx equals zero.

    • a = -2
    • a = 0
    • a = -4
    • a = 2

  18. Let F(x) = integral from 0 to x of (t^2 - 1) dt. Which values of x give stationary points of F?

    • x = 1 only
    • x = 0 and x = 1
    • x = -1 and x = 1
    • x = 0 only

  19. The area under y = 1/x^2 from x = 1 to x = b equals 1/2. What is b?

    • 2
    • sqrt(2)
    • 1/2
    • 4

  20. A curve y = f(x) lies above the x-axis for 0 <= x <= 4, and the integral of f from 0 to 4 is 10. What is the area between the curve and the x-axis?

    • 4
    • 40
    • -10
    • 10

All AQA Maths quizzes